(CNN) Republican Sen. Lindsey Graham of South Carolina told CNN on Tuesday that President Donald Trump asked him while they were playing golf over the weekend: "You wouldn't want to be attorney general, would you?"
Graham, who's positioned himself as vocal Trump ally on Capitol Hill, said he responded: "No, I wouldn't give this up for anything."
Trump responded, according to Graham: "Yeah, I didn't think so -- that would be kind of stupid."
Graham, laughing, described Trump as joking when asking the question.
Former South Carolina Gov. Nikki Haley announced Tuesday that she was stepping down as US ambassador to the United Nations at the end of the year, leading some to speculate that several top Cabinet-level officials could rotate or leave their position to fill the vacancies.
The South Carolina senator, who's up for re-election in 2020, told CNN he would say "no" if Trump asked him to serve in the Cabinet.
"I told him when we were playing golf: You don't want me in the Cabinet," Graham said. "I don't want to be in the Cabinet. He likes me, I like him. Sometimes we disagree. I got the best job in town. You can do like 100 things here. I ain't going nowhere. If the people of South Carolina keep me, I'll stay."
Graham, who could be on track to be the Senate Judiciary Committee chairman, also told CNN he would be inclined to not move on any Supreme Court nominee in 2020 once the presidential primary season starts. Senate Majority Leader Mitch McConnell is leaving that option open in 2020, breaking from his past refusal to move on President Barack Obama's nominee, Merrick Garland.
"I'd be very inclined to take it into the next election," Graham said. "I'd be inclined -- once primary season starts to take it into the next presidency."
Trump was asked by a reporter earlier Tuesday if Graham was "popular enough" to be his next attorney general.
"He is somebody that never asked me that question," Trump responded. "I think he's very happy where he is. He's having a good time. And he really stepped it up. He's doing great."